Trajectories through temporal networks

Abstract

What do football passes and financial transactions have in common? Both are networked walk processes that we can observe, where records take the form of timestamped events that move something tangible from one node to another. Here we propose an approach to analyze this type of data that extracts the actual trajectories taken by the tangible items involved. The main advantage of analyzing the resulting trajectories compared to using, e.g., existing temporal network analysis techniques, is that sequential, temporal, and domain-specific aspects of the process are respected and retained. As a result, the approach lets us produce contextually-relevant insights. Demonstrating the usefulness of this technique, we consider passing play within association football matches (an unweighted process) and e-money transacted within a mobile money system (a weighted process). Proponents and providers of mobile money care to know how these systems are used—using trajectory extraction we find that 73% of e-money was used for stand-alone tasks and only 21.7% of account holders built up substantial savings at some point during a 6-month period. Coaches of football teams and sports analysts are interested in strategies of play that are advantageous. Trajectory extraction allows us to replicate classic results from sports science on data from the 2018 FIFA World Cup. Moreover, we are able to distinguish teams that consistently exhibited complex, multi-player dynamics of play during the 2017–2018 club season using ball passing trajectories, coincidentally identifying the winners of the five most competitive first-tier domestic leagues in Europe.

Circulation of a digital community currency

“…This includes other community currencies 6,16,17,21 as well as major global cryptocurrencies 19,20,26,40 . Recent methodological advances 10,52 promise to extend applicability also to payment systems that are not themselves full currency systems, such as mobile money systems 10,53,54 , large value payment systems [55][56][57][58][59][60][61] , major banks 12,[62][63][64] , and, in an exciting development, centralized national payment infrastructures [65][66][67] or central bank digital currencies 68 . Modern economic infrastructure makes detailed observation possible, and the circulation of money can be studied as (interconnected) networks of monetary flow.…”

“…However, modern payment infrastructure is increasingly digital 5 , and the circulation of money is leaving real-time records on the servers of financial institutions worldwide. These transaction records offer especially high granularity in time and in space, and open up the possibility of fined-grained data-driven studies of financial ecosystems [6][7][8][9][10][11][12] . In this paper we consider the question of how best to study the circulation of money as observed in transaction records.…”

Sarafu Community Inclusion Currency 2020–2021

“…That the observation period extends well into the COVID-19 pandemic is especially relevant, as community currencies tend to have higher utility during economic and/or financial crises 1 , 3 , 4 , 19 , 25 , 27 . More broadly, this dataset serves as a detailed account of an innovative digital currency system of relevance to research topics like digital and financial inclusion 28 – 32 or informal credit and insurance arrangements 15 , 26 , 33 , 34 .…”

“…Datasets such as the one described in this paper allow for empirical observation at higher granularity 1 , 39 – 42 with the potential to inform modelling of currencies and payment systems 43 – 47 . Financial transactions are also an example of real-world walk processes on networks; this dataset will support the development of novel techniques for temporal network analysis 32 , 48 . It will be of particular interest for studying economic networks, where transaction data could be used to explore the relation between network topology, trading dynamics, and allocation of resources 34 , 49 – 54 .…”

“…Future researchers may find it desirable to consider also data from other sources, such as official statistics, public health surveillance, or representative surveys (e.g., FinAccess 16 or Financial Inclusion Insights 55 ). Indeed, doing so would enable research into digital and financial inclusion 28 – 32 , informal credit and insurance arrangements 15 , 26 , 33 , 34 , economic growth and disruption 3 , 4 , 18 , and other relevant topics in development. The values of area_name provided in the user dataset generally correspond to past or present administrative areas in Kenya, making linkage possible.…”